Coefficient inequalities and Hankel determinant for a new subclass of q-starlike functions
Abstract In this study, for 0 < q < 1 $0< q<1$ , we first introduce a function φ q ( τ ) = e q τ − 1 q ( 1 − q τ ) $\varphi _{q}\left ( \tau \right ) = \frac{e^{q\tau }-1}{q\left ( 1-q\tau \right ) }$ and prove that φ q ( τ ) $\varphi _{q}\left ( \tau \right ) $ is convex univalent in th...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2025-08-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13660-025-03337-z |
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| Summary: | Abstract In this study, for 0 < q < 1 $0< q<1$ , we first introduce a function φ q ( τ ) = e q τ − 1 q ( 1 − q τ ) $\varphi _{q}\left ( \tau \right ) = \frac{e^{q\tau }-1}{q\left ( 1-q\tau \right ) }$ and prove that φ q ( τ ) $\varphi _{q}\left ( \tau \right ) $ is convex univalent in the open unit disk U $\mathcal{U}$ for all q ∈ ( 0 , 0.32 ) $q\in \left ( 0,0.32\right ) $ . Further, using the subordination technique and considering q-difference operator, we define a new subclass S φ ∗ ( q ) $S_{\varphi }^{\ast }(q)$ of q-starlike functions associated with a function 1 + φ q ( τ ) $1+\varphi _{q}\left ( \tau \right ) $ , which is in the class P $\mathcal{P}$ . Some new geometric properties, such as coefficient bounds, Feketo–Szego inequalities, and the upper bound of the second-order Hankel determinant, are investigated for the function h belonging to the class S φ ∗ ( q ) $S_{\varphi }^{\ast }(q)$ . |
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| ISSN: | 1029-242X |